{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "scheduled-verification",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7f54704cd820>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "a = np.asarray([[1,2],[3, 4]])\n",
    "a = a/np.sum(a,axis=1)[:,None]  # Normalize\n",
    "\n",
    "plt.pcolor(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "gentle-notice",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7f54704b12b0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolor(a.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "earned-french",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
